3. If f( x) and g( x) are strictly increasing( or decreasing) function on [ a, b ], then gof( x) is strictly increasing( or decreasing) function on [ a, b ].
4. If one of the two functions f( x) and g( x) is strictly increasing and other a strictly decreasing, then gof( x) is strictly decreasing on [ a, b ].
5. If f( x) is continuous on [ a, b ], such that f‘( c) ≥ 0( f ‗( c) > 0) for each c ∈( a, b) is strictly increasing function on [ a, b ].
6. If f( x) is continuous on [ a, b ] such that f ‗( c) ≤( f ‗( c) < 0) for each c ∈( a, b), then f( x) is strictly decreasing function on [ a, b ].
Maxima and Minima of Functions 1. A function y = f( x) is said to have a local maximum at a point x = a. If f( x) ≤ f( a) for all x ∈( a – h, a + h), where h is somewhat small but positive quantity.
The point x = a is called a point of maximum of the function f( x) and f( a) is known as the maximum value or the greatest value or the absolute maximum value of f( x). 2. The function y = f( x) is said to have a local minimum at a point x = a, if f( x) ≥ f( a) for all x ∈
( a – h, a + h), where h is somewhat small but positive quantity.